# Potential energy

1. Feb 8, 2015

### oldspice1212

1. The problem statement, all variables and given/known data
The net force on the mass is the central force F(r) = -k(r-a). Find the potential energy U(r).
a is the spring of natural length and k is spring constant k.

2. Relevant equations
-dU/dx = F(x)

3. The attempt at a solution
$$F(r) = - \frac{ dU }{ dr } implies -k(r-a) = - \frac{ dU }{ dr }$$
So I did this and then integrating both sides I got
$$\frac{ kr^2 }{ 2} - kar = U(r)$$ but this doesn't make much sense when I graph it out, as it gives me a parabola, and I would be expecting a asymptotic type function?

2. Feb 8, 2015

### Brian T

Well think about what happens when r > a and r < a. Both states have potential energy and would therefore be parabolic with the vertex at r = a

P. S. I can't see your pics because I'm on my phone

3. Feb 8, 2015

### oldspice1212

I didn't upload any pics, was just making sure, and yes that makes sense, thank you :)

4. Feb 8, 2015

### Brian T

Last edited: Feb 9, 2015
5. Feb 8, 2015

### oldspice1212

Yes, that's must easier to see! Thank you so much!